The majority of optical channels utilized in premise networks such as local area networks (LAN) or storage area networks (SAN) utilize intensity modulated lasers, where the transmitters modulate the power or intensity of the light. Vertical-cavity surface-emitting laser (VCSEL) transceivers widely deployed in data centers are examples of intensity modulated transceivers, where on-off keying (OOK) is used. VCSEL transceivers have certain advantages including low cost, high reliability, and low power consumption compared to some other types of lasers used in communication systems.
Commercially available VCSEL transceivers with emission wavelengths closely centered around 850 nm, typically 850 nm±10 nm, can support data rates up to 10 Gbps and 14.025 Gbps for Ethernet and Fiber Channel applications, respectively, for channel lengths less than 400 m. Moreover, industry standards for SAN operating at 25 Gbps and 28 Gbps over reduced channel lengths are expected to be released in the future. However, there are limitations to increasing data rates using VCSELs operating at a central wavelength of 850 nm.
As demand for higher data rates continues to grow, the pursuit of cost effective and efficient methods to increase transmission capacity are actively underway. The attributes of some of these transmission methods include WDM, spatial division multiplexing using parallel fiber optics, and advance modulation formats that allow more spectral efficiency than OOK. However, difficulties still exist when attempting to operate at increased data rates. For example, for the aforementioned approaches it is challenging to make reliable VCSELs operating in the 850 nm spectral window fast enough to achieve data rates above 40 Gbps.
It is known by those skilled in the art that VCSEL modulation rates may be increased via the incorporation of indium into material composition of the laser quantum well structure. However, so doing results in the increase of the laser emission wavelength.
Multimode fibers (MMFs) deployed in data centers and premises networks are currently optimized for a narrow spectral window around 850 nm, or less commonly around 1300 nm. These laser-optimized MMFs typically have a core diameter of about 50 μm and modal bandwidth (i.e., EMB) ranging from 2000 MHz·km to at least 4700 MHz·km when measured at 850 nm.
An important dispersive phenomenon in an MMF is a result of modal and chromatic dispersion, and can be described as follows. With respect to chromatic dispersion, a pulse launched into a given mode propagates at a group velocity of the mode and if the pulse has a finite spectral width, the pulse spreads out in time due to material (or chromatic) dispersion. Chromatic dispersion is caused by the wavelength dependence of the material refractive index and results in a difference in propagation speeds for each of the spectral components comprising the transmitted pulse. Chromatic dispersion increases with spectral width and in high-speed VCSELs, the RMS spectral width can be as broad as 0.65 nm. Consequently, in high-speed VCSEL-MMF channels, the chromatic dispersion can become a significant penalty limiting the allowable reaches for accurate transmission.
With respect to modal dispersion, when several mode groups are excited and propagate through the fiber, the transmitted pulse broadens due to differences in mode group velocities transporting the optical signal. These differences can be attributed to imperfections in the refractive index profile and/or differences between the ideal and actual operating wavelength(s) of a transmitter. In laser-optimized fibers the refractive index profile is designed to equalize the mode group delays (or speeds) for the supported mode groups, thereby reducing modal dispersion and increasing the modal bandwidth.
The parameter that describes the refractive index profile is the α-parameter, and the refractive index profile is often referred to as the α-profile. In general, the refractive index profile is a distribution of refractive indices of materials within an optical fiber and for the core of an MMF the profile is defined by a function given by:
                              n          ⁡                      (            r            )                          =                              n            1                    ⁢                                    1              -                              2                ⁢                                                      Δ                    ⁡                                          (                                              r                        a                                            )                                                        α                                                                                        (        1        )            where Δ≈(n1−n2)/n1, n1 is the refractive index on the axis of the fiber (i.e., at the center of the core), n2 is the refractive index in the cladding, r is the radial position inside the fiber core, a is the core radius, and a is the exponent parameter which typically takes a value of ˜2 for fibers designed to support operation near 850 nm.
From equation (1), one can derive a simplified expression for the relative mode group delay tg as a function of the wavelength and the α-profile parameters as shown:
                                          t            g                    ⁡                      (            λ            )                          =                                                            N                1                            ⁡                              (                λ                )                                      c                    [                                                    Δ                ⁡                                  (                                                            α                      -                                                                        α                          opt                                                ⁡                                                  (                          λ                          )                                                                                                            α                      +                      2                                                        )                                            ·                                                (                                                            v                      g                                                              v                      T                                                        )                                                  α                  /                                      (                                          α                      +                      2                                        )                                                                        +            …                    ⁢                                          ]                                    (        2        )            
where c is the speed of light in the vacuum, g is the mode group (MG) index (a mode group can comprise those modes that have nearly equal propagation constants), vg is the number of modes inside the MG that have a propagation constant larger than βg(v), vT is the total number of modes, N1 is the group refractive index of the core material at r=0 and, λ is the optical source wavelength.
The optimum alpha value αopt that minimize group delay at a single operational wavelength λ and y the profile dispersion parameter are given by
                                                        α              opt                        ⁡                          (              λ              )                                =                      2            +                          y              ⁡                              (                λ                )                                      -                          Δ              ⁢                                                                    (                                          4                      +                                              y                        ⁡                                                  (                          λ                          )                                                                                      )                                    ⁢                                      (                                          3                      +                                              y                        ⁡                                                  (                          λ                          )                                                                                      )                                                                    5                  +                                      2                    ⁢                                                                                  ⁢                                          y                      ⁡                                              (                        λ                        )                                                                                                                                ⁢                                  ⁢                  where          ,                                    (        3        )                                          y          ⁡                      (            λ            )                          =                              -                                          2                ⁢                                                                  ⁢                                  n                  1                                                            N                1                                              ⁢                      λ            Δ                    ⁢                                    d              ⁢                                                          ⁢              Δ                                      d              ⁢                                                          ⁢              λ                                                          (        4        )            
Using equations (2-4) the peak effective modal bandwidth valued of λp can be approximated to:
                              λ          p                ≈                              -                          (                              α                -                2                            )                                ⁢                                    (                                                                    2                    ⁢                                                                                  ⁢                                          n                      1                                                                            Δ                    ⁢                                                                                  ⁢                                          N                      1                                                                      ⁢                Δ                ⁢                                                      d                    ⁢                                                                                  ⁢                    Δ                                                        d                    ⁢                                                                                  ⁢                    λ                                                              )                                      -              1                                                          (        5        )            
The modal bandwidth of laser-optimized MMF is characterized by measuring its differential mode delay (DMD) or effective modal bandwidth; metrics standardized within domestic and international standards organizations and known to those skilled in the relevant art. The DMD test method describes a procedure for launching a temporally short and spectrally narrow pulse (reference pulse) from a single-mode fiber (SMF) into the core of an MMF at various radial offsets. After propagating through the MMF, the pulses are received by a photodetector which captures the MMF core power. After removal of the reference pulse temporal width, the DMD temporal width can be determined at the 25% threshold level between the first leading edge and the last trailing edge of all traces encompassed between specified radial positions. The EMB is estimated by the Fourier domain deconvolution of the input pulse from a weighted sum of the received signals for each radial offset launch. The set of weight values utilized in the computation can belong to a set of ten representative VCSELs.
The relation between modal bandwidth, total bandwidth, and the fiber design parameters can be obtained from equation (2). In this equation, the magnitude of the term (α−αopt) is proportional to the mode group delays and therefore inversely related with modal bandwidth. On the other hand the sign of (α−αopt) determines the tilt or slope of the group delays with increasing radial offsets which is important for the computation of the modal-chromatic dispersion interaction (MCDI) and total bandwidth when this fiber is utilized with VCSEL based transceivers as described below.
To illustrate this concept and further clarify the meaning of the DMD slope and sign, consider the two simulated alpha-profile MMFs shown in FIG. 1. In this figure the horizontal axis is the relative time delays (ps/m) of the excited radial mode groups measured at the detector. The vertical axis represents the mode group pulse waveform amplitude for each radial offset of the SMF launch fiber. The lines inside each DMD pulse represent the discrete mode groups of the fibers, which are identical in both DMD plots (a) and (b). For each DMD plot one can compute a least square error (LSE) line connecting the pulses' centroids. The sign of the connecting line slope can be utilized to classify the fibers as left-shifted (L-MMF) (i.e., negative slope), or right-shifted (R-MMF) (i.e., positive slope). Since the magnitudes of the slopes of the radial pulse centroids for these two simulated fibers are identical, the DMD and calculated modal bandwidth (EMB) are the same.
For the L-MMF (negative DMD slope) higher order modes travel faster than lower order modes as can be observed from their shorter arrival time to the detector, herein referred to as negative relative group delay. Conversely, for the R-MMF (positive DMD slope) higher order modes travel slower than lower order modes.
In VCSEL-MMF channels the estimation of the total channel bandwidth depends on the interaction of the spectral dependent coupling of the VCSEL modes to the fiber modes. This coupling produces a mode spectral bias (MSB), where shorter VCSEL wavelengths tend to couple into higher order fiber modes and longer VCSEL wavelengths tend to couple into lower order fiber modes. Consequently, the difference in mode group delays is a result of both modal and chromatic dispersion effects. The effect of MSB on group velocity is summarized Table I:
TABLE IMCDI: Effect of MSB in MMF mode speed.SpectraMMFEffect onModesMMF Mode SpectraGroup VelocityHigher orderTransport energy of lower regions of theReducedmodesVCSEL spectrum (Shorter wavelengths)velocityLower orderTransport energy of higher regions of theIncreasedmodesVCSEL spectrum (Longer wavelengths)velocity
In general, MSB leads to MCDI which, depending on the α-profile, can either increase or reduce the total channel bandwidth. In order to utilize MCDI to increase the channel bandwidth the group velocities of the higher-order modes (HOMs) must propagate faster than the lower-order modes (LOMs) when measured at the operational wavelength of the VCSEL based transceiver. This condition produces a DMD profile and slope sign similar to the one shown in FIG. 1 for the L-MMFs. Since HOMs carry the shorter wavelengths of the VCSEL spectrum, it is possible to compensate for their reduced speed caused by chromatic dispersion effects. When combined with the propagation speed of the LOMs, the resultant speeds of the modes tend to equalize as they propagate in the MMF. This modal-chromatic dispersion interaction and compensation has been further detailed in Gholami A., Molin, D., Sillard, P., “Physical Modeling of 10 GbE Optical Communication Systems,” IEEE OSA JLT, 29(1), 2011, pp. 115-123; J. Castro, R. Pimpinella, B. Kose, and B. Lane, “Investigation of the Interaction of Modal and Chromatic Dispersion in VCSEL-MMF Channels,” IEEE OSA JLT, 30(15), pp. 2532-2541; R. Pimpinella, J. Castro, B/Kose, and B. Lane, “Dispersion Compensated Multimode Fiber,” Proceeding of the 60th IWCS 2011; and J. Castro, R. Pimpinella, B. Kose, and B. Lane, “Mode Partition Noise and Modal-Chromatic Dispersion Interaction Effects on Random Jitter,” IEEE OSA JLT, 31(15), pp. 2629-2638, all of which are incorporated herein by reference in their entirety. A summary of the effect of MSB on channel bandwidth is presented in Table II:
TABLE IIEffect of mode spectral bias and DMD slopesign on channel bandwidth.FiberWithout MSBWith MSBL-MMFHOM propagateReduced mode group velocity differencesfaster than LOMbetween HOMs and LOMs. ImprovedbandwidthR-MMFLOM propagateIncreased mode group velocity differencesfaster than HOMbetween HOMs and LOMs. Reducedbandwidth
By intentionally compensating for modal and chromatic dispersion, benefits in achievable channel reach and bit error rate (BER) performance in L-MMF compared to R-MMF have been modeled and observed. In MMF channels using VCSEL based transceiver, it has been shown that MCDI can be used to not only reduce inter-symbol interference (ISI) penalties but also the mode partition noise (MPN). Conventional industry standard link models predict that MPN becomes an important penalty for longer reaches or higher data rates. An example of the improvements of BER when using L-MMF is shown in FIG. 2. In particular, this figure shows measured BER performance of a 10 G VCSEL transceiver with 0.45 nm spectral width using two fibers with the same modal bandwidth of 4550 MHz·km and the same length 550 m but with opposite sign on the group delay slope. The L-MMF is represented by the solid trace. The R-MMF is represented in the dash trace. Typical gains of 2.5 dB in the optical budget have been observed experimentally with modal-chromatic dispersion compensated fibers depending on the running applications.
In MMF channels (such as for example VCSEL-MMF channels) operating at higher speeds, longer wavelengths, or in coarse-WDM (CWDM) systems, it would be advantageous to preserve the modal-chromatic dispersion compensation properties of current L-MMF. However, in conventional MMFs, the magnitude and sign of the mode group delay has high dependence on wavelength. Using current OM4 fibers it is not possible to maintain the L-MMF characteristics for the broad wavelength range required by CWDM. For example, assuming that an EMB of ≈4700 MHz·km is required by the application, the fiber behaves as L-MMF only in the spectral window of 815 nm to 850 nm.
This is further described with reference to FIG. 3 which shows a simulated SiO2 MMF doped with GeO2 (4.5 mol %) in the core and fluorine (1% WT) in the cladding, where Δ≈0.01 at 850 nm. The utilized a value for this MMF is 2.049 which maximizes the EMB at λp=850 nm. The profile dispersion parameter and the optimum alpha are computed using equations (3-4) and are shown, respectively, on the left and right of FIG. 3. As can be seen from the figure, both of these values decrease monotonically as a function of increasing wavelength. The maximum EMB occurs at λp=850 nm, where α=αopt. This condition produces the cancellation of the modal dependent terms in equation (2). Therefore, the group delays are equalized for all mode groups. As the wavelength varies, αopt becomes larger or smaller than α producing negative or positive group delays as shown in equation (2). Therefore the same MMF can behave as an L-MMF or an R-MMF depending on relative position of the wavelength with respect to λp. More specifically, for wavelengths below λp the DMD tilts to the left, as shown on the left side of FIG. 1, and therefore the fiber can be classified as a L-MMF with modal-chromatic dispersion compensation properties. On the other hand, for wavelengths over λp the DMD tilts to the right and the fiber becomes a R-MMF, increasing total dispersion and degrading total channel bandwidth.
Using the mode group delays obtained via equation (2) and assuming the power distribution of the modes for ten representative VCSELs as described in the known DMD/EMB test standards, it is possible to estimate the EMB as a function of wavelength as shown in FIG. 4. This model is illustrated for a typical MMF construction with λp=850 nm and indicates that L-MMF properties (shaded area) and therefore modal-chromatic compensation can be provided in a limited spectral width that is less than 40 nm.
The simulated behavior is consistent with multiple experiments performed using MMFs of different grades: OM3 and OM4. In these experiments the EMB was measured at different wavelengths ranging from 800 nm to 960 nm, and the results of these measurements are shown in FIG. 5. In all cases, the L-MMF condition occurs only when the measured wavelength was below the λp of each fiber (wavelength for peak EMB of each fiber). When an EMB>4700 MHz·km is required the spectral window for L-MMF becomes relatively limited.
An example of this characteristic is shown in FIGS. 6A and 6B which illustrate a typical MMF using Ge as a main dopant to increase the refractive index in the core. This dopant produces a monotonically decreasing alpha optimum distribution as shown by the solid line in FIG. 6A. When using αd (illustrated by the dashed line) as the α-profile value for the fiber's refractive index, negative relative group delays are attained when αd<αopt. As a result, the high modal bandwidth for negative relative group delays (or L-MMF condition) is maintained for a relatively narrow spectral region. This is shown in FIG. 6B where the negative relative group delays are exhibited to the left of the peak EMB wavelength.
Based on the foregoing, existing approaches do not provide means to optimize modal bandwidth while at the same time produce MCDI for a broad range of optical wavelength. As such, there is a need to provide an improved MMF capable not only for large modal bandwidth, but also negative tg in a broad spectral window.